Probability Quizzes: Test Your Understanding of Chance and Probability

Question 1

In a standard deck of 52 cards, what is the probability of drawing a card that is either a heart or a king?

Accepted Answer

7/26

Answer

1/4

Answer

13/52

Answer

1/2

Question 2

Which of the following is a type of continuous probability distribution?

Accepted Answer

Normal

Answer

Binomial

Answer

Poisson

Answer

Negative binomial

Question 3

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Variance

Answer

Skewness

Answer

Correlation coefficient

Question 4

Which of the following sampling methods is likely to produce a biased sample?

Accepted Answer

Convenience sampling

Answer

Simple random sampling

Answer

Stratified sampling

Answer

Systematic sampling

Question 5

What is the probability of rolling a number greater than 3 on a standard six-sided die?

Accepted Answer

1/3

Answer

1/2

Answer

2/3

Answer

1/6

Question 6

Two fair coins are tossed. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/8

Question 7

A fair coin is tossed 3 times. What is the probability of getting precisely 2 heads?

Accepted Answer

3/8

Answer

1/2

Answer

1/4

Answer

1/8

Question 8

A bag contains 5 red balls and 3 blue balls. If 3 balls are drawn at random, with replacement, what is the probability that all three balls will be red?

Accepted Answer

1/8

Answer

1/4

Answer

1/2

Answer

3/8

Question 9

A fair coin is tossed 5 times. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/8

Question 10

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If 2 balls are drawn at random, with replacement, what is the probability that the first ball is red and the second ball is blue?

Accepted Answer

3/20

Answer

1/4

Answer

1/2

Answer

3/4

Question 11

Bayes' theorem is primarily used to calculate:

Accepted Answer

The probability of an event given that another event has occurred.

Answer

The probability of an event occurring more than once.

Answer

The probability of two events occurring simultaneously.

Answer

The probability of an event occurring in the future.

Question 12

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability that it is not blue?

Accepted Answer

3/5

Answer

1/2

Answer

2/5

Answer

1/5

Question 13

The variance of a probability distribution is:

Accepted Answer

The average squared difference between the random variable and its mean.

Answer

The square of the standard deviation.

Answer

The range of possible values of the random variable.

Answer

The sum of the probabilities of all possible outcomes.

Question 14

Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.4, what is P(A union B)?

Accepted Answer

0.70

Answer

0.12

Answer

0.21

Answer

0.30

Question 15

What is the sample space when rolling a fair six-sided die?

Accepted Answer

{1, 2, 3, 4, 5, 6}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 2, 3, 4}

Answer

{0, 1, 2, 3, 4, 5, 6}

Question 16

Which of the following is NOT a feature of a normal distribution?

Accepted Answer

Mode and median are equal to the mean

Answer

Bell-shaped curve

Answer

Symmetrical around the mean

Answer

The area under the curve from -∞ to +∞ is 1

Question 17

A box contains 5 red balls and 3 blue balls. Two balls are drawn at random, with replacement. What is the probability that the first ball drawn is blue and the second ball drawn is red?

Accepted Answer

3/10

Answer

1/2

Answer

1/4

Answer

1/5

Question 18

Which of the following is a property of conditional probability?

Accepted Answer

The probability of an event given that another event has occurred cannot exceed 1.

Answer

The probability of an event given that another event has occurred is always positive.

Answer

The probability of an event given that another event has occurred is equal to the probability of the other event.

Answer

The probability of an event given that another event has occurred is independent of the probability of the other event.

Question 19

A box contains 10 balls numbered from 1 to 10. Two balls are drawn at random without replacement. What is the probability of drawing the balls with numbers 5 and 7 in that order?

Accepted Answer

1/50

Answer

1/100

Answer

1/200

Answer

1/400

Question 20

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 21

A fair six-sided die is rolled. What is the probability of rolling an even number?

Accepted Answer

1/2

Answer

1/3

Answer

2/3

Answer

3/4

Question 22

A box contains 6 black marbles, 4 white marbles, and 2 red marbles. If three marbles are drawn randomly with replacement, what is the probability of drawing 2 black marbles and 1 white marble?

Accepted Answer

1/12

Answer

1/9

Answer

1/18

Answer

1/27

Question 23

Bayes' theorem is used to:

Accepted Answer

Calculate the probability of an event based on prior knowledge.

Answer

Determine the probability of two dependent events occurring.

Answer

Find the standard deviation of a probability distribution.

Answer

Test the validity of a statistical model.

Question 24

Which of the following is a characteristic of a probability distribution?

Accepted Answer

The sum of probabilities of all events is 1.

Answer

The probability of an event can be negative.

Answer

The mean of a probability distribution is always less than the median.

Answer

The standard deviation of a probability distribution can be negative.

Question 25

When rolling a balanced six-sided die, what is the probability of obtaining a 6?

Accepted Answer

1/6

Answer

1/5

Answer

1/3

Answer

1/4

Question 26

What is the primary purpose of Bayes' theorem?

Accepted Answer

Updating probabilities based on new information.

Answer

Calculating probabilities of compound events.

Answer

Predicting future events.

Answer

Determining probabilities of sequential events.

Question 27

A survey reveals that 60% of individuals prefer coffee over tea. If 45% prefer green tea, what is the probability of a person who prefers green tea also indicating a preference for coffee?

Accepted Answer

(0.45 * 0.60) / 0.45

Answer

0.45 + 0.60

Answer

(0.45 + 0.60) / 0.45

Answer

0.45 * 0.60

Question 28

Define the expected value of a discrete random variable.

Accepted Answer

The average of all possible outcomes, weighted by their probabilities.

Answer

The most probable outcome.

Answer

The sum of all possible outcomes.

Question 29

In a company with branches A and B, branch A has 60 employees with 20% being female. Branch B has 40 employees with 30% being female. If an employee is randomly selected, what is the probability of selecting a female employee?

Accepted Answer

(0.20 * 60 + 0.30 * 40) / (60 + 40)

Answer

0.20 * 0.30

Answer

0.20 + 0.30

Answer

(0.20 + 0.30) / (60 + 40)

Question 30

What is the probability of rolling a 6 on a fair six-sided dice?

Accepted Answer

1/6

Answer

1/3

Answer

1

Answer

1/2

Question 31

A bag contains 8 balls: 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability of drawing a red ball first and then a blue ball?

Accepted Answer

5/12

Answer

1/2

Answer

1/6

Answer

5/8

Question 32

A fair coin is tossed three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

3/8

Answer

1/8

Answer

5/8

Question 33

What is the probability of drawing a face card (jack, queen, or king) from a standard deck of 52 cards?

Accepted Answer

3/13

Answer

1/5

Answer

1/6

Answer

1/3

Question 34

A box contains 6 red, 4 blue, and 2 green marbles. If two marbles are drawn at random with replacement, what is the probability of drawing a red marble and then a green marble?

Accepted Answer

12/60

Answer

1/3

Answer

1/12

Answer

1/4

Question 35

A bag contains 3 red, 2 blue, and 1 green marble. If two marbles are drawn at random without replacement, what is the probability of drawing a red marble and then replacing it before drawing a blue marble?

Accepted Answer

3/10

Answer

1/2

Answer

1/5

Answer

2/5

Question 36

What is the mode of the following data set: 5, 7, 5, 3, 7, 9, 5?

Accepted Answer

5

Answer

7

Answer

3

Answer

9

Question 37

A fair coin is tossed 8 times. What is the probability of obtaining at least 5 heads?

Accepted Answer

240/256

Answer

120/256

Answer

200/256

Answer

160/256

Question 38

Which of the following is a principle of probability?

Accepted Answer

The sum of the probabilities of all possible outcomes is equal to 1.

Answer

The probability of an event not occurring is equal to 2 minus the probability of the event occurring

Answer

The probability of an event occurring is between 0 and 2

Question 39

A fair coin is tossed three times. What is the probability of getting at least two heads?

Accepted Answer

3/4

Answer

1/4

Answer

1/2

Answer

1/8

Question 40

What is the probability of rolling a sum of 7 or 11 on a pair of dice?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/2

Question 41

A company claims that 90% of its products are defect-free. If a random sample of 100 products is taken, what is the probability that exactly 95 of the products are defect-free?

Accepted Answer

0.0287

Answer

0.0143

Answer

0.1148

Answer

0.0574

Question 42

A box contains 6 balls, of which 3 are red and 3 are blue. If two balls are drawn from the box without replacement, what is the probability that the first ball drawn is red and the second ball drawn is blue?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 43

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If two balls are drawn at random, with replacement, what is the probability that at least one ball is red?

Accepted Answer

1 - (3/10) * (2/10)

Answer

(5/10) * (5/10)

Answer

1 - (5/10) * (5/10)

Answer

(3/10) * (2/10)

Question 44

A bag contains 5 red balls, 4 blue balls, and 3 green balls. If two balls are drawn at random, with replacement, what is the probability of drawing a red ball first and then a blue ball?

Accepted Answer

(5/12) * (4/12)

Answer

(4/12) * (5/12)

Answer

(5/12) * (3/12)

Answer

(3/12) * (5/12)

Question 45

A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

Accepted Answer

6/36

Answer

7/36

Answer

5/36

Answer

4/36

Question 46

A survey is conducted among 200 students, of which 120 are male. If a student is selected at random, what is the probability that the student is female?

Accepted Answer

0.4

Answer

0.7

Answer

0.6

Answer

0.5

Question 47

A box contains 6 different colored marbles: red, orange, yellow, green, blue, and purple. If 3 marbles are drawn at random, without replacement, what is the probability of drawing a red marble, then a yellow marble, and then a blue marble?

Accepted Answer

(1/6) * (1/5) * (1/4)

Answer

(1/5) * (1/4) * (1/3)

Answer

(1/6) * (1/4) * (1/3)

Answer

(1/6) * (1/5) * (1/3)

Question 48

A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn at random, with replacement. Let A be the event of drawing a red marble first, and B be the event of drawing a blue marble second. Are events A and B independent?

Accepted Answer

Yes

Answer

Not enough information given

Answer

Only if the first marble is replaced

Answer

No

Question 49

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

10/32

Answer

15/32

Answer

5/32

Answer

20/32

Question 50

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a face card (jack, queen, or king)?

Accepted Answer

12/52

Answer

20/52

Answer

16/52

Answer

8/52

Question 51

A survey is conducted to determine the percentage of people who own a pet. Of the 100 people surveyed, 65 own a pet. What is the point estimate for the population proportion of people who own a pet?

Accepted Answer

0.65

Answer

0.55

Answer

0.75

Question 52

A researcher wants to test the hypothesis that the average height of a certain population is greater than 170 cm. A sample of 50 people is taken, and their average height is found to be 172 cm with a standard deviation of 5 cm. Using a significance level of 0.05, what is the p-value for this test?

Accepted Answer

0.0228

Answer

0.0456

Answer

0.0342

Answer

0.0114

Question 53

A company claims that their new software reduces the time it takes to complete a task by an average of 10 minutes. A sample of 25 tasks is taken, and the average time taken to complete the task using the new software is found to be 9 minutes with a standard deviation of 2 minutes. Using a significance level of 0.05, can we conclude that the company's claim is true?

Accepted Answer

Yes

Answer

Only if the sample size is increased

Answer

Not enough information given

Answer

No